| | | |

## Operator $(\alpha,m)$-convex functions and applications for synchronous and asynchronous functions

#### Erdal ÜNLÜYOL [1] , Yeter ERDAŞ [2] , Seren SALAŞ [3]

In this study, firstly the definition of operator $(\alpha,m)$-convex function is defined. Secondly, a new lemma is given. Then, new theorems are obtained in terms of this lemma. Finally, they are applied for synchronous and asynchronous functions.

The Hermite-Hadamard inequality, $(\alpha¸m)$-convex functions, synchronous and asynchronous functions, Hilbert space, selfadjoint operator, operator $(\alpha¸m)$-convex functions
• \bibitem{Furita} Furuta, T., Hot, L. M., $Pe\breve{c}ari\acute{c}$, J. and Seo, Y., Mond-$Pe\breve{c}ari\acute{c}$ Method in Operator Inequalites. Inequalites for Bounded Selfadjoint Operators on a Hilbert space. Element, Zagreb, 2005.
• \bibitem{Mihesan} Mihe\c{s}an, V. G., A generalization of the convexity, Seminar on Functionel Equations, Approx Convex, Cluj-Napoca (Romania), 1993.
• \bibitem{MN} Moslehian, M. S. and Najafi, H., Around operator monotone functions. \emph{Integr. Equ. Oper. Theory.}, 2011, 71:575-582.
• \bibitem{Dra} Dragomir, S. S., The Hermite-Hadamard type inequalites for operator convex functions. \emph{Appl. Math. Comput.}, 2011, 218(3):766-772.
• \bibitem{YES} Erda\c{s}, Y., Unluyol, E. and Sala\c{s}, S., The Hermite-Hadamard Type inequalities for operator $m$-convex functions in Hilbert Space, \emph{Journal of New Theory}, 5(2015), 80-91.
• \bibitem{Y.E.S} Sala\c{s}, S., Unluyol, E. and Erda\c{s}, Y., The Hermite-Hadamard Type Inequalities for Operator p-Convex Functions in Hilbert Space, \emph{Journal of New Theory}, 4(2015), 74-79.
• \bibitem{R} Rooin, J., Alikhani, A. and Moslehian, M.S., Operator $m$-convex functions. \emph{Georgian Math. J.} 25(2018), no.1, 93-107.
• \bibitem{G3} Ghazanfari, A. G., The Hermite-Hadamard type inequalities for operator $s$-convex functions, \emph{JARPM}, Vol:6, Issue:3, 2014, 52-61.
• \bibitem{GB} Ghazanfari, A. G. and Barani, A., Some Hermite-Hadamard type inequalities for the product of two operator preinvex functions. Banach \emph{J. Math. Anal.} 9(2015), no.2, 9-20.
• \bibitem{SSC} Dragomir, S. S., $\breve{C}eby\breve{s}ev's$ type inequalities for functions of selfadjoint operators in Hilbert spaces, \emph{Linear and Multilinear Algebra}, 58(2010) no. 7-8, 805-814.
• \bibitem{YES1} Erda\c{s}, Y., Unluyol, E. and Sala\c{s}, S., Some new inequalities of operator $m$-convex functions and applications for Synchronous-Asynchronous functions, accepted and press 2019 in \emph{Complex Anal. Oper. Theory}.
Primary Language en Articles Author: Erdal ÜNLÜYOL Author: Yeter ERDAŞ Author: Seren SALAŞ Publication Date : October 15, 2019
 Bibtex @research article { mathenot634516, journal = {Mathematical Sciences and Applications E-Notes}, issn = {}, eissn = {2147-6268}, address = {}, publisher = {Murat TOSUN}, year = {2019}, volume = {7}, pages = {225 - 236}, doi = {10.36753/mathenot.634516}, title = {Operator \$(\\alpha,m)\$-convex functions and applications for synchronous and asynchronous functions}, key = {cite}, author = {ÜNLÜYOL, Erdal and ERDAŞ, Yeter and SALAŞ, Seren} } APA ÜNLÜYOL, E , ERDAŞ, Y , SALAŞ, S . (2019). Operator $(\alpha,m)$-convex functions and applications for synchronous and asynchronous functions. Mathematical Sciences and Applications E-Notes , 7 (2) , 225-236 . DOI: 10.36753/mathenot.634516 MLA ÜNLÜYOL, E , ERDAŞ, Y , SALAŞ, S . "Operator $(\alpha,m)$-convex functions and applications for synchronous and asynchronous functions". Mathematical Sciences and Applications E-Notes 7 (2019 ): 225-236 Chicago ÜNLÜYOL, E , ERDAŞ, Y , SALAŞ, S . "Operator $(\alpha,m)$-convex functions and applications for synchronous and asynchronous functions". Mathematical Sciences and Applications E-Notes 7 (2019 ): 225-236 RIS TY - JOUR T1 - Operator $(\alpha,m)$-convex functions and applications for synchronous and asynchronous functions AU - Erdal ÜNLÜYOL , Yeter ERDAŞ , Seren SALAŞ Y1 - 2019 PY - 2019 N1 - doi: 10.36753/mathenot.634516 DO - 10.36753/mathenot.634516 T2 - Mathematical Sciences and Applications E-Notes JF - Journal JO - JOR SP - 225 EP - 236 VL - 7 IS - 2 SN - -2147-6268 M3 - doi: 10.36753/mathenot.634516 UR - https://doi.org/10.36753/mathenot.634516 Y2 - 2019 ER - EndNote %0 Mathematical Sciences and Applications E-Notes Operator $(\alpha,m)$-convex functions and applications for synchronous and asynchronous functions %A Erdal ÜNLÜYOL , Yeter ERDAŞ , Seren SALAŞ %T Operator $(\alpha,m)$-convex functions and applications for synchronous and asynchronous functions %D 2019 %J Mathematical Sciences and Applications E-Notes %P -2147-6268 %V 7 %N 2 %R doi: 10.36753/mathenot.634516 %U 10.36753/mathenot.634516 ISNAD ÜNLÜYOL, Erdal , ERDAŞ, Yeter , SALAŞ, Seren . "Operator $(\alpha,m)$-convex functions and applications for synchronous and asynchronous functions". Mathematical Sciences and Applications E-Notes 7 / 2 (October 2019): 225-236 . https://doi.org/10.36753/mathenot.634516 AMA ÜNLÜYOL E , ERDAŞ Y , SALAŞ S . Operator $(\alpha,m)$-convex functions and applications for synchronous and asynchronous functions. Math. Sci. Appl. E-Notes. 2019; 7(2): 225-236. Vancouver ÜNLÜYOL E , ERDAŞ Y , SALAŞ S . Operator $(\alpha,m)$-convex functions and applications for synchronous and asynchronous functions. Mathematical Sciences and Applications E-Notes. 2019; 7(2): 236-225.

Authors of the Article
[3]